Algorithm for vector autoregressive model parameter estimation using an orthogonalization procedure
Algorithm for vector autoregressive model parameter estimation using an orthogonalization procedure
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DOI：
10.1114/1.1454134
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发表时间：
2002-02-01
影响因子：
3.8
通讯作者：
Sato, S
中科院分区：
文献类型：
--
作者：
Bagarinao, E;Sato, S
本文回顾了由Korenberg首先提出的快速正交搜索算法的推导过程，重点介绍了它在向量自回归模型的系数矩阵估计问题中的应用。研究了以前未考虑的算法的新方面。其中之一是应用该算法来估计具有时变系数的矢量自回归过程的系数矩阵，当所述过程有多种实现时，还进行了计算机模拟以表征估计的统计特性。结果表明，即使对于较短的时间序列，该算法也能很好地估计出自调参数。统计特征表明，估计的标准差减小为1/rootN （N为时间序列的长度），这是最小二乘估计的典型行为。该方法的另一个关键方面是它直接扩展到向量非线性自回归模型的参数估计。可以在模型中加入非线性项，并使用相同的算法有效地估计其相关参数。利用由洛伦兹方程产生的混沌时间序列，该算法产生一个模型，该模型捕获了数据的非线性结构，并表现出与原始系统相同的混沌吸引子。(C) 2002生物医学工程学会。
We review the derivation of the fast orthogonal search algorithm, first proposed by Korenberg, with emphasis on its application to the problem of estimating coefficient matrices of vector autoregressive models. New aspects of the algorithm not previously considered are examined. One of these is the application of the algorithm to estimate coefficient matrices of a vector autoregessive process with time-varying coefficients when multiple realizations of the said process are available, Computer simulations were also performed to characterize the statistical properties of the estimates. The results show that even for shorter time series the algorithm works well and obtains good estimates of the tune-varying parameters. Statistical characterization indicates that the standard deviation of the estimates decreases as 1/rootN (N being the length of the time series), a typical behavior of least-squares estimators. Another key aspect of the approach, which has previously been considered, is its direct extension to the parameter estimation of vector nonlinear autoregressive models. Nonlinear terms can be added to the model and the same algorithm can be applied to effectively estimate their associated parameters. Using chaotic time series generated from the Lorenz equations, the algorithm produces a model that captures the nonlinear structure of the data and exhibits the same chaotic attractor as that of the original system. (C) 2002 Biomedical Engineering Society.